diffeology

English

Noun

diffeology (plural diffeologies)

1. (differential geometry) The set of smooth parametrizations of a given set $X$; the set of smooth maps $S\rightarrow X$, where $S$ is any open set $\subseteq \mathbb {R} ^{n}$; the theory of such constructs.
   • 2007, Jan Kubarski, Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann; on the Occasion of the Hundredth Anniversary of His Birthday, page 358:

     In this case, $A$ and $f(A)$ are both D-open and $f:A\rightarrow f(A)$ is a diffeomorphism where $A$ and $f(A)$ are equipped with their subset diffeology.

   • 2010, Patrick Iglesias-Zemmour, The Moment Maps in Diffeology, American Mathematical Society, page 32:

     And, for ${\mathcal {G}}^{*}/\Gamma$ and ${\mathcal {G}}'^{*}/\Gamma '$ equipped with the quotient diffeologies, $h_{\Gamma }^{*}$ is naturally smooth.

Usage notes

• The dimensional qualifier n is not required to be the same for all members of the diffeology.
• A member of a diffeology may be called a plot.
• A set together with a diffeology is called a diffeological space.

Derived terms

• quotient diffeology

Related terms

• diffeological

See also

• diffeological space

Further reading

• diffeology on Wikipedia.Wikipedia